Summary: Optimal Two­Dimensional Compressed Matching
Amihood Amir \Lambda Gary Benson y Martin Farach z
Georgia Tech Mt Sinai School of Med Rutgers & DIMACS
Abstract
Recent proliferation of digitized data and the unprecedented growth in the volume of stored
and transmitted data motivated the definition of the compressed matching paradigm. This
is the problem of efficiently finding a pattern P in a compressed text T without the need to
decompress.
We present the first optimal two­dimensional compressed matching algorithm. The compres­
sion under consideration is the two dimensional run­length compression, used by FAX transmis­
sion.
We achieve optimal time by proving new properties of two­dimensional periodicity. This
enables performing duels in which no witness is required. At the heart of the dueling idea lies
the concept that two overlapping occurrences of a pattern in a text can use the content of a
predetermined text position or witness in the overlap to eliminate one of them. Finding witnesses
is a costly operation in a compressed text, thus the importance of witness­free dueling.
Key words: Matching, two­dimensional, witness, periodicity, compression
1 Introduction
Recent developments in multimedia have led to an unprecedented increase in digitally stored infor­
mation. This increase and the projected growth in the volume of telecommunications have made it

Source: Amir, Amihood - Computer Science Department, Bar Ilan University

Collections: Mathematics